A modification of the factorization method for the classical acoustic inverse scattering problems

It is well-known that sampling type methods for solving inverse scattering problems fail if the wave number is an eigenvalue of a corresponding interior eigenvalue problem. By adding the far field patterns corresponding to an artificial ball lying within the obstacle and imposing an impedance bounda...

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Bibliographic Details
Published inInverse problems Vol. 30; no. 3; pp. 35013 - 14
Main Authors Kirsch, Andreas, Liu, Xiaodong
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.03.2014
Subjects
acoustic scattering
Boundaries
eigenvalue
Eigenvalues
Factorization
Far fields
impenetrable obstacle
Inverse scattering
Mathematical models
method
Obstacles
Sampling
Wavelengths
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Summary:It is well-known that sampling type methods for solving inverse scattering problems fail if the wave number is an eigenvalue of a corresponding interior eigenvalue problem. By adding the far field patterns corresponding to an artificial ball lying within the obstacle and imposing an impedance boundary condition on the boundary of this ball we propose a modification of the factorization method which provides the characterization of the unknown obstacle for all wave numbers. Some numerical experiments are presented to demonstrate the feasibility and effectiveness of our method.
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ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/30/3/035013